There’s no question that Albert Pujols is one of the greatest players in the history of Major League Baseball. As the active leader in wOBA (.434) and wRC+ (169), it’s not easy to come up with a superlative that sounds like hyperbole for Pujols. But a commenter on his stats page gave it a try last week:

ALBERT Einstein had an IQ of 160. That means he is 60% more intelligent than the average human.

Albert Pujols has a wRC+ of 177 during the past 3 seasons. That means he is 77% better at the plate than the average big leaguer.

He is so much better at the plate than the average player, than Einstein was than the average human. And we all know how damn intelligent Einstein was!

Even forgetting that comparing baseball skill to smarts is apples and oranges and Intelligence Quotient is an imperfect measure of mental ability—especially when the figure is just an estimation for someone who never took an official test (at least, not publicly)—this is nonsense because that’s not how I.Q.’s are scored. But that’s not to say we can’t examine this theory more systematically.

I.Q. scores don’t reflect proportions of intelligence; someone with an I.Q. of 200 isn’t twice as smart as an average human. Instead, tests are scored on a bell curve of an approximately normal distribution with mean µ = 100 and standard deviation σ = 15.

Retroactive I.Q. estimators are dubious, but the 160 score that this commenter used seems to be the most widely accepted figure for Einstein. That puts him exactly four standard deviations from the mean, meaning he was smarter than 99.9968% of the world’s population. In other words, 1 out of every 31,250 people is as smart as Albert Einstein.

In order to put Pujols on a comparable scale, we must construct a distribution function to express his talent as a percentile instead of a proportion. Among the 242 MLB players who came to bat at least 1,000 times from 2008-10, the average wRC+ was µ ~ 106.2 with standard deviation σ ~ 19.5.

That means Pujols’ 177 wRC+ over the last three seasons is 3.63 standard deviations from the mean. Assuming for simplicity’s sake that wRC+ can be accurately expressed with a normal distribution function, The Machine comes out at the 99.9858th percentile—only 1 in 7,042 people could reach that level.

Viewed in this light, it’s clear that Pujols is a truly exceptional ballplayer, but a comparison to the father of modern physics is wrong. Unfortunately for Einstein, there’s one big problem that renders these results inconclusive: humongous sample bias.

When we examined Einstein’s brainpower, we did so relative to the I.Q. scores of the entire human population—the mean represented John Q. Public, not the average theoretical physicist or Nobel laureate. Pujols, on the other hand, was being compared to the best baseball players in the country, if not the world; the data comes from players who were good enough not just to get to the big leagues, but to receive substantial playing time over a three-year period.

If we make the generous assumption that 1 out of every 100 people on the planet is good enough to play in the MLB, Pujols jumps to the 99.999858th percentile. That’s 4.68 standard deviations from the mean—or, more dramatically, a wRC+ of 177 for every 704,225 people.

In a world of 6.9 billion people, there should be 220,800 people who can match or best Einstein’s 160 I.Q. If we narrow the scope of Pujols’ competitors to 947—the number of players who had at least 20 PA’s from 2008-10—there should be 0.1345 players of Prince Albert’s caliber in the majors, or 1 for every 51.3 billion people on Earth. A hitter this good should not exist.

Obviously, Einstein’s work was much more important than what Pujols has done—a game-winning homer in Game 5 of the NLCS doesn’t quite compare to E=mc2. Moreover, there are legitimate questions to be raised about the usefulness of evaluating one of the greatest geniuses of all time by an I.Q. test he never took. And these findings are as inapplicable to serious analysis as this study is unscientific.

Take this all with a huge grain of salt, but relatively speaking (get it? because it’s Einstein), Albert Pujols’ ability to hit baseballs seems to be more unique than the mental capacities of one of the most influential intellectuals in human history.

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Fun read! See? Math CAN be fun 🙂

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7 years ago

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Kampfer

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This is really impressive!!
One must appreciate just how rare is a Albert Pujols and the fact that we have the chance to witness his legacy

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7 years ago

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Nick

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Albert Pujols is above average at best

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7 years ago

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sassifras

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But what are the odds of them both being called Albert?

Gotta say, though, that I disagree with the idea that there are over 200,000 people currently alive as smart as Einstein…seems a bit unlikely, and falsified by the very fact that we are choosing Einstein as our benchmark for insane statistical freaks.

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7 years ago

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rotofan

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Fun commentary and a nice application of statistics.

I have just one suggested tweak: Avoid a modifier for the word unique. Either something is unique or it is not. Or substitute another word for unique, such as unusual, which can be modified, or better yet, a single word that captures your intended meaning, such as rarer.

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7 years ago

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James Holzhauer

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wRC+ is not normally distributed.

“A hitter this good should not exist.” What a terrible conclusion. There are six players ahead of him in career wRC+. If you get seven 1-in-50 billion anomalies, it’s time to re-examine your methodology. (That doesn’t even account for the absurd probability of a hitter achieving Babe Ruth’s wRC+ if we assume a normal distribution.)

IQ measurements are also horribly flawed at the genius level, but that’s neither here nor there.

“a nice application of statistics.” Whoever said this has never taken a stats class or at least didn’t pay attention in it.

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7 years ago

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Pat

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There’s also the issue that IQ measures, or supposedly measures, general levels of intelligence, but it’s being compared to a statistic which measure a specific type of athleticism, baseball skill. It would wRC+ would need to be compared to some metric measuring Physics ability. No such metric exists currently, but that’s hardly an excuse.

The fact the Einstein is generally considered the second greatest physicist of all time should hint at a flaw in this analysis.

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7 years ago

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Not James Holzhauer

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“And these findings are as inapplicable to serious analysis as this study is unscientific.”

I never claimed this was perfect. Anyone taking this seriously enough to be offended by possible flaws in my methodology is perhaps a bit too emotionally invested in a comparison that is impossible to accurately perform and would have no practical application.

Relax. It’s supposed to be fun.

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7 years ago

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Physicist

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IQ is not a comparable stat to WRC. If there is a stat that measures raw athleticism, that would be the one to compare to IQ. You need a result based stat. Perhaps Einstein’s paper’s impact factors or H-factor?

Than we can make awesome statements such as:
Einstein: Landau as Albert Pujols: Ryan Howard

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7 years ago

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NBarnes

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Without wanting to jump in quite as aggressively as Mr. Holzhauer, I, too, paused at the line “there should be 0.1345 players of Prince Albert’s caliber in the majors, or 1 for every 51.3 billion people on Earth. A hitter this good should not exist.” Pujols is fantastic and historic, but he’s not actually the best hitter to ever play baseball. He’s not even second best. He spent half his career as the second best active player, let alone all-time. Something is wonky with the methodology.

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7 years ago

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TheGrandSlamwich

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“a game-winning homer in Game 5 of the NLCS doesn’t quite compare to E=mc2”

This is the only part I take issue with. The only thing physics did for me was help me meet an ex-girlfriend in college! And keep me rooted on earth and not float away into space… I’ll take the Homerun!

Great article. I don’t know why people didn’t catch the joking nature of it.

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7 years ago

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Matt Goldfarb

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Isn’t the point of community research to HELP each-other complete the research? How does bashing an 18-19 yr old kid (who, let’s not forget, took his own time to try to answer an impossible question and post his findings and methods online) for a few (inevitably) flawed assumptions help anyone or anything? I am by NO MEANS an advocator of the idea that “if you don’t have something nice to say, say nothing at all,” HOWEVER; those of you jumping down Lewie’s throat are 100% out of line and should be ashamed for your conduct within one of the best… Read more »

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Articles like this that purport to compare the talents of people in totally different occupations should not be taken seriously from a results point of view, but that doesn’t mean that they can’t be pretty valuable as teaching tools. The author starts out by taking someone else’s simplistic comparison of Einstein’s intelligence to Pujuls’ baseball skills and explores it. Along the way he uses and discusses some statistical concepts, such as standard deviation. He draws a conclusion (1 in 51 billion!) but with many disclaimors along the way. This is simply a whimsical thought exercise demonstrating how one might approach… Read more »

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7 years ago

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Ez

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I knew Pujols wasn’t real.

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7 years ago

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Bill

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Well the probability of every interaction since the birth of man conspiring to bring me here at this exact moment is so ridiculously small as to make the fact that I’m here impossible too.

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Constructive Criticism: One big assumption you should rework is that everyone in the world has had a desire to play baseball at a high level. Your baseball playing populous is much smaller than the world population and would result in Pujols looking less impressive. Otherwise, this is a fun article.

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7 years ago

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glassSheets

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The potential baseball playing populous is the world populous. If Albert Pujols never played baseball, he would still be “capable” of doing what he is doing. The fact that Pujols advanced his baseball skill through desire to play baseball doesnt make his baseball ability less in comparison to those who have never even heard of the game. If I did nothing (like sit in a plain white room with nothing but a bed) my entire life, I would do quite poorly on an IQ test. I would not be able to write, move my hands, or read the question, but… Read more »

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7 years ago

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glassSheets

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Typos.. I would get a score presumably higher than 0 now.

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7 years ago

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lzii01

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Two of my favorite people, Albert Pujols and Albert Einstein, in the same article! Lewie, I only wish I had a daughter so she could marry you.

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7 years ago

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RichP

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This was an amusing analysis, fun but not meaningful.

In the real world, Gaussian statistics are often a poor model of reality, especially at several sigma and up. And, I compare the Einstein IQ estimate of 160 to models of IQ v SAT scores, and I believe a lot of 160+ IQ’s exist every year in the US.

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7 years ago

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Anthony

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I think there are people “as smart” as einstein. They just don’t apply themselves. I know a guy who had his college tuition paid for by being really smart and was going to a fairly prestigious college. 2 years later he’s at home working in a factory because he smoked himself (pot) out of college and was too lazy to go to class. That said, the same can be said for baseball. I would not be surprised that if everyone on the planet fullfilled their baseball potential that there would be some people better than albert pujols. Not that much… Read more »

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7 years ago

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Worldtour

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